The present application relates generally to an improved data processing apparatus and method and more specifically to mechanisms for rapidly estimation of temperature rise in wires due to Joule heating.
Joule heating is the process by which the passage of an electric current through a conductor releases heat. Joule heating is referred to as ohmic heating or resistive heating because of its relationship to Ohm's Law. It forms the basis for the myriad of practical applications involving electric heating. In applications where heating is an unwanted by-product of current use (e.g., load losses in electrical transformers) the diversion of energy is often referred to as resistive losses.
A typical integrated circuit package comprises a package having connections to input/output pins, interconnect layers, a substrate, and a heat sink. Within a package, wires in the interconnect layer experience poor heat transfer due to low thermal conductivity of inter-layer dielectric and not being close enough for the heat sink to remove heat. Self heating depends on root mean square (IMS) current density. Self heating of wires lowers meant time to failure (MTF) and worsens wire delay (higher resistance). Self heating of wires may also cause thermomigration due to thermal gradients.
Electromigration is the transport of material caused by the gradual movement of the ions in a conductor due to the momentum transfer between conducting electrons and diffusing metal atoms. The effect is important in applications where high direct current densities are used, such as in microelectronics and related structures. As the structure size in electronics such as integrated circuits (ICs) decreases, the practical significance of this effect increases. Electromigration and Joule heating concerns worsen with technology scaling. Currents flowing through the wires do not scale proportional to wire dimensions. Low-k dielectrics and higher resistivity due to surface scattering aggravate the problem.
Prior art methods for estimating temperature rise due to Joule heating are based on the well-known duality between thermal and electrical phenomena. The prior art methods usually consider only simple physical geometries and heat flow paths. These methods are not applicable to cases with arbitrary wire geometries and thermal couplings between nets. In addition, these prior art methods are not very accurate due to various simplifying assumptions.
Other prior art methods are based on numerical thermal analysis, such as the finite element methods for solving partial differential equations (PDEs). These methods usually are not extendable for full-chip self heating analysis in millions of nets.